Problem 7:
Let $ABC$ be a triangle with $AC > AB$: Let $P$ be the intersection point of the perpendicular bisector of $BC$ and the internal angle bisector of $\angle CAB$: Let $X$ and $Y$ be the feet of the perpendiculars from $P$ to lines $AB$ and $AC$ respectively. Let $Z$ be the intersection point of lines $XY$ and $BC$: Determine the value of \[\frac{BZ}{ZC}\]
BdMO National Higher Secondary 2010/7
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nafistiham
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Re: BdMO National Higher Secondary 2010/7
the angle bisector of any angle and the perpendicular bisector of the opposite side of it intersects at the circumcircle.and, feet of perpendiculars from any point of the circumcircle on the sides of the inscribed triangle are collinear.which is called the wallace line.so,
\[\frac{BZ}{ZC}=1\]
\[\frac{BZ}{ZC}=1\]
- wallace line.JPG (35.55KiB)Viewed 2925 times
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.